Joint Embedding Variational Bayes

VJE (Variational Joint Embedding) is a non-contrastive self-supervised learning framework that maximizes a symmetric conditional ELBO over paired encoder embeddings without reconstruction.

It defines a conditional likelihood directly on the target representations, applying a Student-t distribution to polar representations to handle uncertainty in the representation space.

• The directional term models only angular agreement on the unit sphere.
• The radial term separately handles agreement in embedding magnitude.
• This decomposition mitigates norm-induced pathology and provides a valid variational bound on the directional factor.

On the inference side, an amortized inference network with a diagonal Gaussian posterior shares feature-wise variance with the directional likelihood, expressing anisotropic uncertainty without a separate projection head.

On ImageNet-1K, CIFAR-10/100, and STL-10, it showed competitive performance against standard non-contrastive baselines under linear probe and k-NN evaluation, and also delivered strong results on OOD detection using the representation-space likelihood.

In summary, this is a TMLR 2026 paper that reformulates representation learning as a probabilistic model while also presenting uncertainty interpretation in the representation space and the potential for downstream OOD applications.